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Just Opposite

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

Mystic Rose

Age 14 to 16
Challenge Level
How many lines are drawn at each stage of construction of the mystic rose?
Now look at the completed mystic rose - can you describe how many lines are drawn from each point?
How do these relate to "Alison's method" and "Charlie's method"?